In order to maintain running stability of an electric drive vehicle, it is necessary to estimate a friction characteristic accurately and control wheel speed so that each wheel can achieve an appropriate slip ratio with respect to the friction characteristic. The friction characteristic mentioned herein means the relation between a slip ratio of a drive wheel and a friction coefficient between the wheel and a road surface or a physical amount (for example, a drive force of the drive wheel) equivalent to the friction coefficient. For example, Patent Literature 1 has been known as a technique for estimating a friction characteristic between a wheel and a road surface and controlling torque to maximize the drive force during acceleration running or maximize the brake force during deceleration running by use of the estimation result. Patent Literature 1 is a technique in which a slip ratio of each drive wheel is calculated from detected values of wheel speeds of the drive wheel and a corresponding driven wheel, a friction coefficient is further calculated from a ground load of the drive wheel and a drive force of the drive wheel in a travelling direction, and a gradient of the friction coefficient relative to the slip ratio is calculated by use of the friction coefficient and the slip ratio.